Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

"Vegeu el resum a l'inici del document del fitxer adjunt."

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

"Vegeu el resum a l'inici del document del fitxer adjunt."

Sobolev mappings: Lipschitz density is not an isometric invariant of the target

"Vegeu el resum a l'inici del document del fitxer adjunt."

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Preference intensities and risk aversion in school choice: a laboratory experiment

We experimentally investigate in the laboratory two prominent mechanisms that are employed in school choice programs to assign students to public schools. We study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the Gale-Shapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play "safer" strategies under the Gale-Shapley but not under the Boston mechanism. Both results have important implications for the efficiency and the stability of the mechanisms.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

High bi-atrial organization in patients with long-standing persistent atrial fibrillation terminated within the left atrium

Sustained atrial fibrillation (AF) is maintained by sites displaying high dominant frequency (DF). In patients (pts) with long-standing persistent AF (LS-pAF), their spatial distribution and the presence of a left-to-right atrial DF gradient remain poorly known. We hypothesized that the pre-ablation bi-atrial frequency characteristics of LS-pAF pts terminated within the left atrium (LT) are different from that of non terminated (NT) ones. Methods: 23 consecutive pts (59±7y, LS-pAF duration 19±12m) underwent stepwise catheter ablation (step-CA) consisting in pulmonary veins isolation, left atrial (LA) defragmentation, and right atrial (RA) ablations for non terminated AF. A quadripolar catheter (CAT) was placed into the RA appendage (RAA), a decapolar CAT into the coronary sinus (CS) and a duodecapolar CAT into the LA divided into 8 segments. For each segment, 20-sec of bipolar recording was acquired. The DF was defined as the largest peak in the power spectrum (3-15 Hz). The inter-atrial DF gradient was defined as the DF difference between LA and RA appendages. Results: LS-pAF was terminated in 83% (19/23) of the pts: 17 LT, 2 during RA ablation and 4 NT. The figure shows that before ablation bi-atrial DF values of LT pts are significantly lower than that of NT pts for each LA segment as well as for the RAA (p < 0.05). No significant LA-to-RA DF gradient was observed both for LT (0.3±0.5 Hz, p=ns) and NT (0.5±0.03 Hz, p=ns) pts. No significant difference in DF values was observed between LA segments. Conclusions: The lower DF of LT pts is suggestive of a higher organization within both atria compared to NT pts. Our findings suggest that low bi-atrial DF values, but not inter-atrial DF gradient, might be of interest for selecting LS-pAF candidates for sinus rhythm restoration by step-CA.

Human invariant V alpha 24-J alpha Q TCR supports the development of CD1d-dependent NK1.1+ and NK1.1- T cells in transgenic mice.

A sizable fraction of T cells expressing the NK cell marker NK1.1 (NKT cells) bear a very conserved TCR, characterized by homologous invariant (inv.) TCR V alpha 24-J alpha Q and V alpha 14-J alpha 18 rearrangements in humans and mice, respectively, and are thus defined as inv. NKT cells. Because human inv. NKT cells recognize mouse CD1d in vitro, we wondered whether a human inv. V alpha 24 TCR could be selected in vivo by mouse ligands presented by CD1d, thereby supporting the development of inv. NKT cells in mice. Therefore, we generated transgenic (Tg) mice expressing the human inv. V alpha 24-J alpha Q TCR chain in all T cells. The expression of the human inv. V alpha 24 TCR in TCR C alpha(-/-) mice indeed rescues the development of inv. NKT cells, which home preferentially to the liver and respond to the CD1d-restricted ligand alpha-galactosylceramide (alpha-GalCer). However, unlike inv. NKT cells from non-Tg mice, the majority of NKT cells in V alpha 24 Tg mice display a double-negative phenotype, as well as a significant increase in TCR V beta 7 and a corresponding decrease in TCR V beta 8.2 use. Despite the forced expression of the human CD1d-restricted TCR in C alpha(-/-) mice, staining with mCD1d-alpha-GalCer tetramers reveals that the absolute numbers of peripheral CD1d-dependent T lymphocytes increase at most by 2-fold. This increase is accounted for mainly by an increased fraction of NK1.1(-) T cells that bind CD1d-alpha-GalCer tetramers. These findings indicate that human inv. V alpha 24 TCR supports the development of CD1d-dependent lymphocytes in mice, and argue for a tight homeostatic control on the total number of inv. NKT cells. Thus, human inv. V alpha 24 TCR-expressing mice are a valuable model to study different aspects of the inv. NKT cell subset.